Geometry Chapter 1 Vocabulary
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Questions and Answers

What is the definition of a line segment?

A measurable part of a line that consists of two points called endpoints and all the points between them.

What is the definition of a point?

A location. Neither shape nor size.

What is the definition of a segment bisector?

A segment, line, or plane that intersects a segment at its midpoint.

What is the definition of a regular polygon?

<p>A polygon with all congruent angles.</p> Signup and view all the answers

What is the definition of a concave polygon?

<p>A polygon for which there is a line containing a side of the polygon that also contains a point in the interior of the polygon.</p> Signup and view all the answers

What is the definition of an obtuse angle?

<p>An angle with a degree measure greater than 90.</p> Signup and view all the answers

What is the definition of a transversal?

<p>A line that intersects two or more lines at two different points.</p> Signup and view all the answers

What is the definition of skew lines?

<p>Lines that do not intersect and are not coplanar.</p> Signup and view all the answers

What is the definition of corresponding angles?

<p>Angles that lie on the same side of the transversal and on the same side of the line.</p> Signup and view all the answers

What is the definition of alternate interior angles?

<p>Non-adjacent inside angles that lie on opposite sides of the transversal.</p> Signup and view all the answers

What is the definition of inductive reasoning?

<p>A reasoning that uses a number of specific examples to arrive at a conclusion.</p> Signup and view all the answers

What is the definition of a diagonal?

<p>A segment that connects any two nonconsecutive vertices.</p> Signup and view all the answers

What is the definition of a parallelogram?

<p>A quadrilateral with both pairs of opposite sides parallel.</p> Signup and view all the answers

What is the definition of a rhombus?

<p>A parallelogram with 4 congruent sides.</p> Signup and view all the answers

What is the definition of a square?

<p>A parallelogram with 4 congruent sides and 4 right angles.</p> Signup and view all the answers

What is the definition of a trapezoid?

<p>A quadrilateral with one pair of parallel sides.</p> Signup and view all the answers

What is the definition of a midsegment of a trapezoid?

<p>A segment that connects the midpoints of the legs.</p> Signup and view all the answers

What are opposite rays?

<p>Rays that share a common endpoint and are collinear.</p> Signup and view all the answers

What is the definition of a vertex?

<p>A common endpoint of the angle.</p> Signup and view all the answers

What does the term 'undefined terms' mean in geometry?

<p>Words, usually readily understood that are not formally explained by means of more basic words and concepts.</p> Signup and view all the answers

What is a corollary?

<p>A statement that can easily prove using a theorem.</p> Signup and view all the answers

What is a conjecture?

<p>An educated guess.</p> Signup and view all the answers

What is a counter example?

<p>An example used to show that a given statement is not always true.</p> Signup and view all the answers

What is a flow proof?

<p>Uses statements written in boxes and arrows to show the logical progression of an argument.</p> Signup and view all the answers

What are the legs of an isosceles triangle?

<p>Two congruent sides.</p> Signup and view all the answers

What is an included angle?

<p>The angle formed by two sides of a polygon that is a side of each of two angles.</p> Signup and view all the answers

What is an altitude in a triangle?

<p>A segment from a vertex of the triangle to the line containing the opposite side and perpendicular to that side.</p> Signup and view all the answers

What is a perpendicular bisector in a triangle?

<p>A line/segment/ray that passes through the midpoint of a side and is perpendicular to that side.</p> Signup and view all the answers

What is a point of concurrency?

<p>Point of intersection of concurrent lines.</p> Signup and view all the answers

What is an orthocenter?

<p>Lines containing the altitudes of a triangle are concurrent, intersecting at a point.</p> Signup and view all the answers

What is the centroid of a triangle?

<p>Point of concurrency of the medians of a triangle.</p> Signup and view all the answers

What is the circumcenter of a triangle?

<p>Point of concurrency of the perpendicular bisector of a triangle.</p> Signup and view all the answers

What is a median of a triangle?

<p>A line segment with endpoints that are a vertex of a triangle and the midpoint of the side opposite the vertex.</p> Signup and view all the answers

What is indirect reasoning?

<p>Reasoning that assumes that this assumption leads to a contradiction of the hypothesis like a postulate theorem, or corollary.</p> Signup and view all the answers

What are alternate interior angles?

<p>Non-adjacent inside angles that lie on opposite sides of the transversal.</p> Signup and view all the answers

What are the defined terms in geometry?

<p>Terms that are explained using defined terms or other defined terms.</p> Signup and view all the answers

Study Notes

Chapter 1 Vocabulary

  • n-gon: A polygon with n sides
  • Plane: A flat surface that extends indefinitely in all directions
  • Linear pair: Two adjacent angles whose non-common sides are opposite rays
  • Acute angle: An angle with a degree measure less than 90
  • Distance: The length of a segment between two points
  • Angle bisector: A ray that divides an angle into two congruent angles
  • Opposite rays: Rays that share a common endpoint and are collinear
  • Vertical angles: Two nonadjacent angles formed by intersecting lines
  • Construction: A method of creating geometric figures without measuring tools
  • Degrees: A unit of measure used for angles and arcs
  • Vertex: A common endpoint of an angle
  • Ray: Part of a line with one endpoint and extending indefinitely in one direction
  • Undefined terms: Words easily understood, not formally explained
  • Line segment: A measurable part of a line with two endpoints and all points between them
  • Intersection: The set of points common to two or more geometric figures
  • Coplanar: Points lying on the same plane
  • Angle: Formed by two noncollinear rays with a common endpoint
  • Point: A location with no size
  • Line: Made up of points, with no thickness
  • Segment bisector: A segment, line, or plane that intersects a segment at its midpoint
  • Perpendicular: Lines, segments, or rays that form right angles
  • Sides: The rays of an angle
  • Midpoint: The point on a segment exactly halfway between the endpoints
  • Congruent segments/angles: Segments or angles having the same measure
  • Supplementary angles: Two angles whose measures add up to 180
  • Complementary angles: Two angles whose measures add up to 90
  • Collinear: Points lying on the same line

Chapter 2 Vocabulary

  • Polygon: A closed figure formed by a finite number of coplanar segments
  • Perimeter: The sum of the lengths of the sides of a polygon
  • Regular polygon: A polygon with all congruent angles
  • Concave: A polygon with a line containing a side and a point in the interior.
  • Defined terms: Terms explained using other defined terms
  • Obtuse angle: An angle with a degree measure greater than 90
  • Regular polygon: A polygon with all congruent sides
  • Area: The number of square units needed to cover a surface
  • Space: Boundless three-dimensional set of all points
  • Adjacent angles: Two angles lying on the same plane, with a common vertex and side, but no common interior points
  • Alternate Interior Angles: Non-adjacent interior angles that lie on opposite sides of the transversal
  • Point-slope form: y - y₁ = m(x - x₁)
  • Parallel planes: Planes that do not intersect
  • Theorem: A proven statement or conjecture
  • Transversal: A line that intersects two or more lines at different points
  • Consecutive interior angles: Interior angles on the same side of the transversal
  • Statement: A sentence that is either true or false
  • Skew lines: Lines that do not intersect and are not coplanar
  • Slope: Ratio of change in y to change in x
  • Corresponding angles: Angles that lie on the same side of the transversal and on the same side of the lines
  • Parallel lines: Coplanar lines that do not intersect
  • Slope-intercept form: y = mx + b
  • Inductive reasoning: Arriving at a conclusion based on observations
  • Postulate/axiom: A statement that is accepted as true without proof
  • Deductive reasoning: Using facts, rules, definitions, or properties to reach a conclusion

Chapter 3 Vocabulary

  • Formal proof: Statements and reasons arranged in two columns
  • Counter example: Example showing a statement is not true
  • Conjecture: Educated guess
  • Corresponding Parts: Matching parts of congruent polygons
  • Corollary: Statement easily proven using a theorem
  • Vertex angle: The angle between the two sides of a polygon
  • Base angle: Two angles formed by the base and congruent side of an isosceles triangle
  • Auxiliary line: An extra line in a figure to understand geometric relationships
  • Included angle: The angle formed by two sides
  • Flow proof: Statements and reasons connected with boxes and arrows
  • Congruent polygons: Polygons with congruent corresponding parts
  • Exterior angle: Formed by one side and an extension of another side of a triangle
  • Legs/sides of an isosceles triangle: The two equal sides of an isosceles triangle
  • Remote interior angles: The two angles of a triangle not adjacent to the exterior angle
  • Included side: The side of a polygon shared by two angles

Chapter 4 Vocabulary

  • Incenter: Point of concurrency of the angle bisectors of a triangle
  • Altitude: Segment from a vertex to the line containing the opposite side, perpendicular to that side
  • Perpendicular bisector: A line/segment/ray that intersects the midpoint of a side and is perpendicular to that side
  • Point of concurrency: Point of intersection of concurrent lines
  • Orthocenter: Point of concurrency of the altitudes of a triangle
  • Centroid: Point of concurrency of the medians of a triangle
  • Concurrent lines: Three or more lines that intersect at a common point
  • Circumcenter: Point of concurrency of perpendicular bisectors of the sides of a triangle
  • Median: Segment joining a vertex and the midpoint of the opposite side of a triangle
  • Indirect reasoning: Reasoning that leads to a contradiction to prove a statement

Chapter 6 Vocabulary

  • Diagonal: Segment connecting two non-consecutive vertices of a polygon
  • Parallelogram: Quadrilateral with both pairs of opposite sides parallel
  • Rectangle: Parallelogram with four right angles
  • Rhombus: Parallelogram with four congruent sides
  • Square: Parallelogram with four congruent sides and four right angles
  • Trapezoid: Quadrilateral with one pair of parallel sides
  • Bases: Parallel sides of a trapezoid
  • Legs: Non-parallel sides of a trapezoid
  • Base angles: Angles formed by the base and the legs of a trapezoid
  • Isosceles trapezoid: Trapezoid with congruent legs
  • Midsegment of a trapezoid: Segment connecting the midpoints of the legs
  • Kite: Quadrilateral with two pairs of adjacent congruent sides

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Description

Test your understanding of essential vocabulary from Chapter 1 of Geometry. This quiz covers key terms such as n-gon, acute angle, and angle bisector, among others. Perfect for reinforcing foundational concepts in geometry.

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